Theorems · Definition · commutative algebra

Ideal.giMapComap

{R : Type u} →
  {S : Type v} →
    {F : Type u_1} →
      [inst : Semiring R] →
        [inst_1 : Semiring S] →
          [inst_2 : FunLike F R S] →
            (f : F) →
              [inst_3 : RingHomClass F R S] → Function.Surjective ⇑f → GaloisInsertion (Ideal.map f) (Ideal.comap f)

map and comap are adjoint, and the composition map f ∘ comap f is the identity

Defined in

Mathlib.RingTheory.Ideal.Maps

Cited by

6 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringFunLikeRingHomClass